Jonathan Wiggs/The Boston Globe via Getty Images(FALL RIVER, Mass.) -- Former Patriots tight end Aaron Hernandez called his fiancée and told her it was "important" for her to get rid of a box "right away" in the days after his friend was found executed less than a mile from Hernandez's million-dollar mansion, prosecutors said Tuesday.

So Shayana Jenkins, the mother of his 1-year-old daughter, took the box, covered it with baby clothes, stuffed it into a black trash bag, packed it into her sister's car and drove to Plainville, where she tossed it in a dumpster, Bristol County District Attorney Patrick Bomberg told a court Tuesday.

The detail came out during a bail hearing Tuesday for Jenkins, who was indicted on perjury charges and was released on her own personal recognizances.

During the hearing, the court was told that Jenkins was given immunity to testify before the grand jury about the murder of Odin Lloyd.

Her lawyer, Janice Bassil, said her client had been cooperative, but Bomberg painted a different picture of Jenkins' cooperation.

Jenkins was captured on her own home surveillance system walking out of the house with the box on June 18, prosecutors said. She was also captured on video at a Plainville ATM machine, but when confronted with that surveillance footage at the grand jury Jenkins said she did not remember where she went that day, the prosecutor said.

But she told the grand jury she did not remember where she threw the box and that she did not know what was in the box, Bomberg told the court.

"She told the grand jury she dumped it in a dumpster, but she couldn't tell anybody where it was,'' Bomberg said.

Bassil said that it was not unusual for her client to not know what Hernandez was up to.

"Their relationship, in many ways, had what I refer to as a 'don't ask don't tell' aspect," Bassil said. She said that Jenkins preferred to stay in the dark because Hernandez was an athlete and she preferred not to ask him what he did on his own time. "She could spend her life tracking him down every single minute."

Bomberg was not specific about the item in the box, but prosecutors have publicly said they continue to look for the gun used to murder Lloyd, 27, a semi-pro football player. Hernandez is charged with first degree murder in connection with the Lloyd's murder.